By Jennifer Sutton, Kevin Bryan
The complete consultant to the next rating on the
AP Environmental technology exam
About the book:
Introduction
Reviews of the AP examination structure and scoring
Proven options for answering matching; challenge fixing; a number of selection; reason and influence; tables, graphs, and charts; and simple arithmetic questions
Hints for tackling the free-response questions
Part I: topic Reviews
Cover all topic parts you'll be verified on:
Earth's structures and resources
The residing world
Population
Land and water use
Energy assets and consumption
Pollution
Global change
Part II: perform Exams
3 full-length perform tests with solutions and whole explanations
Proven test-taking strategies
Focused stories of all examination topics
3 full-length perform exams
Read or Download CliffsNotes AP Environmental Science PDF
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Additional info for CliffsNotes AP Environmental Science
Sample text
LI. 12. L3. 14. L5. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 50. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. i . [i - ( i . (i 51. 1 INTRODUCTION If 2 is substituted in the equation 3x- 2 = 4 the two sides become equal. We say that x = 2 is a solution of the equation. The following operations are helpful for finding the solu tions of an equation: I. II. The same quantity may be added to or subtracted from both sides of an equation. Both sides of an equation may be multiplied (or divided) by the same non-zero quantity.
To explain the meaning of x , where a is an irrational number, is beyond the scope of this text. But it is worth noting that it is possible to use arbitrary real numbers as exponents, while pre serving all the laws of exponents. a EXAMPLE 4 16 8 1 / 2 2/3 =Vl6 = 4 . ( V5 V5 = 5 3 3 ^ , 2 . 2 5 = 5 1 / 2 1 / 3 2 = 4 9 o r g 2/3 . V? = V5I25 EXAMPLE 5 (2 xV) 2 1 / 2 -2 2 / V / 2 y 6 / 2 - 2x y 2 3 28. 1/4 16 does not equal 4. Beware: EXERCISE SET In fact, 16 1/4 2,3 Simplify each of the following: 1.
Thus, x=0 or x+ 7 = 0 , which yields the solutions x=0 (b) or x = -7 or x - 3 = 0, or x=3 . x - 5x+6 = 0 2 (x- 2)(x- 3) = 0. Thus, x- 2 = 0 which yields the solutions x=2 (c) x - 2x+l = 0 2 (x- l)(x- 1) = 0. Thus, x- 1 = 0 , which yields the solution x= 1 . EXAMPLE 3 S O L V E : 2y = 30- 4y 2 62. SOLUTION W e begin by bringing all terms to the left side 2 y + 4 y - 30 = 0. 2 Dividing by 2, we have y +2y-15 = 0 2 (y+5)(y-3) = 0. Thus, y+ 5 = 0 or y- 3 = 0 , or y=3. which yields the solutions y = -5 The solutions of a quadratic equation 2 ax + bx + c = 0 can always be obtained by the quadratic formula: (3) This formula is not "magic", but has a logical derivation from still another method of solving a quadratic equation called "completing the square".